Sunday, December 15, 2013

Calculated Mean
Global Temperatures 1610-2012

Introduction

This monograph considers only average global temperature. It does not
discuss weather, which is a complex study of energy moving about the planet. It
does not even address local climate, which includes precipitation. It does,
however, consider the issue of Global Warming and the mistaken perception that
human activity has a significant influence on it.

The word ‘trend’ is used here for temperatures in two
different contexts. To differentiate, α-trend applies to averaging-out the
uncertainties in reported average global temperature measurements to produce
the average global temperature oscillation resulting from the net ocean surface
oscillation. The term β-trend applies to the slower average temperature change of the
planet which is associated with change to the temperature of the bulk volume of
the material (mostly water) involved.

The first paper to suggest the hypothesis that the sunspot
number time-integral is a proxy for a substantial driver of average global
temperature change was made public 6/1/2009. The discovery started with
application of the first law of thermodynamics, conservation of energy, and the
hypothesis that the energy acquired, above or below break-even (appropriately accounting
for energy radiated from the planet), is proportional to the time-integral of
sunspot numbers. The derived equation revealed a rapid and sustained global energy
rise starting in about 1941. The true average global temperature anomaly change
β-trend is proportional to global energy change.

Subsequent analysis revealed that the significant factor in
calculating the β-trend is the sunspot number anomaly time-integral. The
sunspot number anomaly is defined as the difference between the sunspot number
in a specific year and an average sunspot number for several years.

Measured temperature anomaly α-trends oscillate above and
below the temperature anomaly β-trend calculated using only the sunspot number anomaly time-integral.

The existence of ocean oscillations, especially the Pacific
Decadal Oscillation, led to the perception that there must be an effective net surface
temperature oscillation for the planet with all named and unnamed ocean oscillations as
participants. Plots of measured average global temperatures indicate that the
net surface temperature oscillation has a period of 64 years with the
most recent maximum in 2005.

Combination of the effects results in the effect of the ocean
surface temperature oscillation (α-trend) decline 1941-1973 being slightly
stronger than the effect of the rapid rise from sunspots (β-trend) resulting in
a slight decline of the trend of reported average global temperatures. The steep
rise 1973-2005 occurred because the effects added. A high coefficient of
determination, R2, demonstrates that the hypothesis is true.

Over the years, several refinements to this work (often resulting from other's comments which may or may not have been corroborative) slightly improved the
accuracy and led to the equations and figures in this paper.

Prior work

The law of conservation of energy is applied effectively the same as described in
Reference 2 in the development of a very similar equation that calculates
temperature anomalies. The difference is that the variation in energy ‘OUT’ has
been found to be adequately accounted for by variation of the sunspot number anomalies.
Thus the influence of the factor [T(i)/Tavg]4 is eliminated.

Change to the level of atmospheric carbon dioxide has no
significant effect on average global temperature. This was demonstrated in 2008
at Reference 6 and is corroborated at Reference 2
and again here.

A substantial contributor to this variation
appears to be the apparent random variation in magnitude and period of el Nino.

Global Warming ended more than a decade ago as shown here,
and in Reference 4 and also Reference 2.

Average global temperature is very sensitive to cloud change
as shown in Reference 5.

The value used for average sunspot number was 43.97 (average
1850-1940) in Ref. 1. It is set at 34 (average 1610-1940) in this paper. The
procession of values for average sunspot number produces slight but steady
improvement in R2 for the period of measured temperatures and
progressively greater credibility of average global temperature estimates for
the period prior to direct measurements becoming available.

The ocean oscillation does
not significantly add or remove planet energy. In the decades immediately
prior to 1941 the amplitude range of the trends was not significantly influenced
by any candidate external forcing fluctuation; so the observed amplitude of the
net ocean surface temperature trend anomaly must be approximately the same as
the amplitude of the average global temperature trend anomaly, which is
approximately 0.36 K and a period of approximately 64 years (verified below).

The AGT trajectory (Figure 1) suggests that the least-biased
simple wave form of the ocean surface temperature oscillation is approximately
saw-toothed. Ignoring the offset for the moment, the sea surface temperature anomaly
oscillation can be described as varying linearly from 0 K in 1909 to approximately
0.36 K in 1941 and linearly back to the 1909 value in 1973. This cycle repeats before
and after with a period of 64 years. This is consistent with the 50-70 year
period previously observed by others.

Because the actual magnitude of the ocean oscillation in any
year is needed, the expression to account for the contribution of the ocean
oscillation to AGT is given by the following:

ΔTosc = (A,y) K (degrees) (i)

where ocean oscillation is the magnitude of the surface
temperature anomaly trend of the oscillation in year y, and A is the maximum magnitude of the ocean
surface temperature trend oscillation.

Equation (i) is graphed in Figure 0.5.

Figure 0.5: Ocean surface
temperature oscillations do not affect the bulk energy of the planet.

Although the peak-to-peak amplitude of the ocean oscillation
is approximately 0.36 K, by definition, ocean
oscillation is symmetrical with respect to zero. Therefore the SST trend oscillation
since before 1900 has been approximately ±0.18 K.

The sunspot number anomaly time-integral drives the temperature anomaly trend

It is axiomatic that change to the average temperature trend
of the planet is due to change to the net energy retained by the planet.

Table 1 in reference 2 shows the influence of atmospheric
carbon dioxide (CO2) to be insignificant (tiny change in R2
if considering CO2 or not) so it can be removed from the equation by
setting coefficient ‘C’ to zero. With ‘C’ set to zero, Equation 1 in Reference
2 calculates average global temperature anomalies (AGT) since 1895 with 89.82%
accuracy (R2 = 0.898220).

The current analysis determined that 34, the approximate
average of sunspot numbers from 1610-1940, provides a slightly better fit (in
fact, the best fit) to the measured temperature data. The influence, of Stephan-Boltzmann radiation change
due to AGT change, on energy change is adequately accounted for by the sunspot
number anomaly time-integral. With these refinements to Equation (1) in Reference 2 the
coefficients become A = 0.3588, B = 0.003461 and D = ‑ 0.4485. R2 increases slightly to 0.904906
and the calculated anomaly in 2005 is 0.5045 K. Also with these refinements the
equation calculates lower early temperature anomalies and projects slightly higher (0.3175 K vs. 0.269 K in 2020) future anomalies. The resulting equation for calculating the
AGT anomaly for any year, 1895 or later, is then:

Anom(y) = (0.3588,y)
+ 0.003461/17 Σyi=1895
(s(i) – 34) – 0.4485 (ii)

Where:

Anom(y) = calculated
temperature anomaly in year y, K

(0.3588,y)
= approximate contribution of ocean cycle effect to AGT in year y

s(i) =
average daily Brussels International sunspot number in year i

Measured temperature anomalies are from Figure 2 of Reference 3. The excellent
match of the up and down trends since before 1900 of calculated and measured temperature anomalies, shown here in Figure 1, demonstrates the usefulness and validity of the
calculations.

Projections until 2020 use the expected sunspot number trend for
the remainder of solar cycle 24 as provided 11 by NASA. After 2020
the limiting cases are either assuming sunspots like from 1925 to 1941 or for
the case of no sunspots which is similar to the Maunder Minimum.

Some noteworthy volcanoes and the year they occurred are also shown
on Figure 1. No consistent AGT response is observed to be associated with
these. Any global temperature perturbation that might have been caused by
volcanoes of this size is lost in the temperature measurement uncertainty.

Much
larger volcanoes can cause significant temporary global cooling from the added
reflectivity of aerosols and airborne particulates. The Tambora eruption, which
started on April 10, 1815 and continued to erupt for at least 6 months, was
approximately ten times the magnitude of the next largest in recorded history
and led to 1816 which has been referred to as ‘the year without a summer’. The
cooling effect of that volcano exacerbated the already cool temperatures
associated with the Dalton Minimum.

Figure 1.1: Same as
Figure 1 but with 5-year running average of measured temperatures.

R2 = 0.973. (Added 5/26/15)

As discussed in Reference 2, ocean oscillations produce
oscillations of the ocean surface temperature with no significant change to the
average temperature of the bulk volume of water involved. The effect on AGT of
the full range of surface temperature oscillation is given by the coefficient
‘A’.

(A, B, C, and D are the coefficients in Equation
1 of Reference 2)

The influence of ocean surface temperature oscillations can
be removed from the equation by setting ‘A’ to zero. To use all regularly
recorded sunspot numbers, the integration starts in 1610. The offset, ‘D’ must
be changed to -0.1993 to account for the different integration start point and
setting ‘A’ to zero. Setting ‘A’ to zero requires that the anomaly in 2005 be
0.5045 - 0.3588/2 = 0.3251 K. The result, Equation (1) here, then calculates
the trend 1610-2012 resulting from just the sunspot number anomaly time-integral.

-0.1993 is
merely an offset that shifts the calculated trajectory vertically on the graph,
without changing its shape, so that the calculated temperature anomaly in 2005
is 0.3251 K which is the calculated anomaly for 2005 if the ocean oscillation
is not included.

Figure 2: Anomaly
trend from just the sunspot number anomaly time-integral using Equation (1).

Average global temperatures were not directly measured in
1610 (thermometers had not been invented yet). Recent estimates, using proxies,
are few. The temperature anomaly trend that Equation (1) calculates for that time is roughly
consistent with other estimates. The decline in the trace 1610-1700 on Figure 2
results from the low sunspot numbers for that period as shown on Figure 2 of
Reference 1.

How this phenomenon
could take place

Although the
connection between AGT and the sunspot number anomaly time-integral is demonstrated,
the mechanism by which this takes place remains somewhat theoretical.

Various papers have been written
that indicate how the solar magnetic field associated with sunspots can influence
climate on earth. These papers posit that decreased sunspots are associated
with decreased solar magnetic field which decreases the deflection of and
therefore increases the flow of galactic cosmic rays on earth.

Henrik Svensmark, a Danish physicist, found that decreased
galactic cosmic rays caused decreased low level (<3 km) clouds and planet
warming. An abstract of his 2000 paper is at Reference 13. Marsden and
Lingenfelter also report this in the summary of their 2003 paper 14 where they make the statement “…solar activity increases…providing more
shielding…less low-level cloud cover…increase surface air
temperature.”

These findings have been
further corroborated by the cloud nucleation experiments 15 at CERN.

These papers associated the increased low-level clouds with increased
albedo leading to lower temperatures. Increased low clouds would also result in
lower average cloud altitude and therefore higher average cloud temperature.
Although clouds are commonly acknowledged to increase albedo, they also radiate
energy to space so increasing their temperature increases radiation to space
which would cause the planet to cool. Increased albedo reduces the energy
received by the planet and increased radiation to space reduces the energy of
the planet. Thus the two effects work together to change the AGT of the planet.

Simple analyses 5 indicate that either an increase of
approximately 186 meters in average cloud altitude or a decrease of average
albedo from 0.3 to the very slightly reduced value of 0.2928 would account for
all of the 20th century increase in AGT of 0.74 °C. Because the
cloud effects work together and part of the temperature change is due to ocean
oscillation, substantially less cloud change is needed.

As a possibility, the period and amplitude of oscillations
attributed to ocean cycles demonstrated to be valid after 1895 are assumed to
maintain back to 1610. Equation (1) is modified as shown in Equation (2) to
account for including the effects of ocean oscillations. Since the expression
for the oscillations calculates values from zero to the full range but
oscillations must be centered on zero, it must be reduced by half the
oscillation range.

The ocean oscillation factor, (0.3588,y) – 0.1794, is
applied to the period prior to the start of direct temperature measurements as a possibility. The
effective sea surface temperature anomaly, (A,y), is defined in Reference 2.

Applying Equation (2) to the sunspot numbers from Figure 2 of
Reference 1 produces the trend shown in Figure 3 next below. Available measured
average global temperatures from Figure 2 in Reference 3 are superimposed on the calculated
values.

Figure 3 shows that temperature anomalies calculated using
Equation (2) estimate possible trends since 1610 and actual trends of reported
temperatures since they have been accurately measured world wide. The match
from 1895 on has R2 = 0.9049 which means that 90.49% of average
global temperature anomaly measurements are explained. All factors not
explicitly considered (such as the 0.09 K s.d.
random uncertainty in reported annual measured temperature anomalies, aerosols, CO2, other non-condensing ghg, volcanoes, ice change, etc.) must find room in that unexplained 9.51%. Note that a
coefficient of determination, R2 = 0.9049 means a correlation
coefficient of 0.95.

A survey 12 of non-tree-ring global temperature
estimates was conducted by Loehle including some for a period after 1610. A
simplification of the 95% limits found by Loehle are also shown on Figure 3.
The spread between the upper and lower 95% limits are fixed, but, since the
anomaly reference temperatures might be different, the limits are adjusted
vertically to approximately bracket the values calculated using the equations.
The fit appears reasonable considering the uncertainty in all values.

Smoothing of the measured temperatures using 5-year moving
average achieved R2 = 0.973. This accounts for most of the random
uncertainty in reported annual measured temperature anomalies with only 2.7%
left unexplained.

Calculated temperature anomalies look reasonable back to 1700 but indicate higher temperatures
prior to that than most proxy estimates. They are, however, consistent with the
low sunspot numbers in that period. They
qualitatively agree with Vostok, Antarctica ice core data but decidedly differ
from Sargasso Sea estimates during that time (see the graph for the last 1000
years in Reference 6). Credible worldwide assessments of average global
temperature that far back are sparse. Ocean oscillations might also have been
different from assumed.

Possible lower values
for average sunspot number

Possible lower assumed values for average sunspot number, with
coefficients adjusted to maximize R2, result in noticeably lower
estimates of early (prior to direct measurement) temperatures with only a tiny
decrease in R2. Calculated temperature anomalies resulting from using an average
sunspot number value of 26 are shown in Figure 4. The projected temperature anomaly trend
decline is slightly less steep (0.018 K warmer in 2020) than was shown in
Figure 1.

Figure 4: Calculated temperature anomalies from the sunspot number anomaly time-integral plus ocean oscillation using 26
as the average sunspot number with superimposed available measured data from
Reference 3 and range estimates determined by Loehle.

Carbon dioxide change
has no significant influence

The influence that CO2 has on AGT can be
calculated by including ‘C’ in Equation (1) of Reference 2 as a coefficient to
be determined. The tiny increase in R2 demonstrates that
consideration of change to the CO2 level has no significant
influence on AGT. The coefficients and resulting R2 are given in
Table 1.

1) Firmly acknowledge the established fact
that gas molecules can absorb/emit photons only at specific discreet
wavelengths (which might be broadened from pressure, etc.). Full spectrum
(Plank’s law) Stephan-Boltzmann (S-B) radiation applies to liquids and solids,
not to gases.

2) From gas kinetics, the time between
atmospheric molecule collisions is extremely short (The Hyperphysics calculator
calculates approximately 0.0001 microsecond at sea level pressure and
temperature).

3) The elapsed time between absorption and
emission of a photon by a CO2 gas molecule must be greater than zero
or there would be no evidence that absorption-emission had occurred.

4) At sea level conditions, some or all of
the photon energy that is absorbed by a ghg molecule is immediately transferred
to other molecules by collision. The process of absorbing a photon and
transferring (thermal conduction in the gas) the added energy to other
molecules is thermalization. A common observation of thermalization by way of
water vapor is that nights cool faster when absolute water vapor content is
lower.

5) The reduced radiation flux on both
sides of the 15 micron CO2 absorption line, as observed in most TOA
measurements 18 results because some of the EMR energy absorbed by
CO2 has been thermalized.

6) Terrestrial radiation is nearly
all in the wavelength range 6-100 microns. Thermalized energy carries no identity of the
molecule that absorbed it.

7) Jostling between the molecules
sometimes causes reverse-thermalization. At low to medium altitudes, EMR
emission stimulated by reverse-thermalization is mostly by way of
water vapor. The spike at 15 microns results from reverse-thermalization to CO2 molecules at
very high altitude.

8) The thermalized radiation warms the
air, reducing its density, causing updrafts which are exploited by soaring
birds, sailplanes, and occasionally hail. Updrafts are matched by downdrafts
elsewhere, usually spread out but sometimes recognized by pilots and passengers
as ‘air pockets’ and micro bursts.

9) The population gradient of ghg
molecules, (especially water vapor above about 3 km, declining with increasing
altitude) favors radiation to space. Ghg molecules that emit a photon are
‘recharged’ by reverse-thermalization.

A forcing adds
energy to earth analogous to speed adding distance on a trip. Both need to
operate for a duration to accumulate any energy change to the planet or
distance on the trip. If the forcing is constant, the energy change is simply
the forcing times the duration. If the forcing varies (or not), the energy
change is the time-integral of the forcing. On the planet, the net energy added
divided by the effective thermal capacitance (consistent units) gives the
average global temperature (AGT) change. Therefore the AGT change is equal to
an appropriate scale factor times the time-integral of the forcing.

Atmospheric
carbon dioxide (CO2), has been considered to be a forcing. If so,
the AGT change attributable to CO2 change must equal an appropriate
scale factor times the time-integral of the CO2 level (or some function thereof). It has been
demonstrated here that CO2 change has no
significant effect on AGT 1895-2012.If CO2 is a
forcing, the temperature could only increase (unless compensated for by an
as-yet-undiscovered forcing which magically disappeared as soon as credible
average global temperature measurements became available). Observation that the
AGT trend ever decreases to an earlier AGT is evidence that the scale factor is
zero, CO2 is not a significant forcing, and something else is
causing the temperature change.

According to
widely available data from Vostok, Antarctica (or any other) ice cores, during previous
glaciations and interglacials, CO2 and AGT went up and down approximately
in lock-step (as so dramatically displayed in An Inconvenient Truth). This demonstrates that, at least up to
about 300 ppmv, CO2 has no significant effect on AGT.

Application of
this analysis methodology to CO2 levels for the entire Phanerozoic
eon (about 542 million years) (Berner, 2001) proves that CO2 levels
up to at least 6 times the present will have no significant effect on AGT.

Some might
assert that there must be a ‘break even’ CO2 level. Above this level
CO2 is a positive forcing and below the break-even level the AGT
trajectory would indicate it was a negative forcing.

Pick any two end
temperatures. A ‘break-even’ CO2 level and offset can be determined
such that the calculation will produce the two end temperatures. However, pick
two different end temperatures and a different ‘break-even’ CO2
level would be calculated. Since the possibility of many different ‘break-even' levels is ludicrous, the conclusion that CO2 has no significant effect
on AGT prevails and something else is causing the temperature change.

Because CO2
is only a trace gas in the atmosphere, if CO2 change does not cause
temperature change, it cannot cause climate change. THUS THE CO2
CHANGE FROM BURNING FOSSIL FUELS HAS NO SIGNIFICANT EFFECT ON CLIMATE and
climate sensitivity (the effect on AGT of doubling CO2) is not
significantly different from zero.

This finding
appears to contradict the known absorption of 15 micron radiation by CO2.
Suspected explanations for this include that there are so many more
'opportunities' for absorption by water vapor molecules (hundreds of absorption
lines per molecule times number of molecules) that the added CO2
'opportunities' have an insignificant effect (single absorption line in the
range of significant terrestrial radiation) and/or added TOA CO2
molecules emitting to space compensate for the added molecules absorbing at low
altitude.

The two factors
which explain the last 300+ years of climate change are also identified in a
peer reviewed paper published in Energy and Environment, vol. 25, No. 8,
1455-1471.

Further discussion of
ocean cycles (Added 6/23/14)

The temperature contribution to AGT of ocean cycles is
approximated by a function that has a saw-tooth trajectory profile. It is
represented in Equation (1) of Reference 2 by (A,y) where A is the total amplitude and y is
the year. The uptrends and down trends are each determined to be 32 years long
for a total period of 64 years. The total amplitude resulting from ocean oscillations
was found here to be 0.3588 K (case highlighted in Table 1).

Thus, for an ocean cycle surface temperature uptrend, the contribution of ocean oscillations
to AGT is approximated by adding (to the value calculated from the sunspot number anomaly time-integral) 0.3588 multiplied by the fraction of the 32 year period that has
elapsed since a low. For an ocean cycle surface temperature down trend, the contribution is calculated by adding
0.3588 minus 0.3588 multiplied by the fraction of the 32 year period that has
elapsed since a high. The lows were found to be in 1909 and 1973 and the highs
in 1941 and 2005. The resulting trajectory, offset by half the amplitude, is shown
as ‘approximation’ in Figure 5.

Temperature data is available for three named cycles: PDO,
ENSO 3.4 and AMO. Successful accounting for oscillations is achieved for PDO
and ENSO when considering these as forcings (with appropriate proxy factors)
instead of direct measurements. As forcings, their influence accumulates with
time. The proxy factors must be determined separately for each forcing. The
measurements are available since 1900 for PDO 16 and ENSO3.4 17.
This PDO data set has the PDO temperature measurements reduced by the average
SST measurements for the planet.

The contribution of PDO and ENSO3.4 to AGT is calculated by:

PDO_NINO = Σyi=1900 (0.017*PDO(i) + 0.009
* ENSO34(i)) (3)

Where:

PDO(i) =
PDO index 16 in year i

ENSO34(i) =
ENSO 3.4 index 17 in year i

How this calculation compares to the idealized approximation
used in Equation (2) is shown in Figure 5. The high coefficient of determination in Table 1 and the comparison in Figure 5 corroborate the assumption that the saw-tooth profile provides an adequate approximation of the influence of all named and unnamed ocean cycles in the calculated AGT anomalies.

Figure 5: Comparison
of idealized approximation of ocean cycle effect and the calculated effect from
PDO and ENSO.

Conclusions

Others that have looked at only amplitude or only duration factors for solar cycles got poor correlations with average global temperature.
The good correlation comes by combining the two, which is what the
time-integral of sunspot number anomalies does. As shown in Figure 2, the temperature anomaly trend
determined using the sunspot number anomaly time-integral has experienced substantial
change over the recorded period. Prediction of future sunspot numbers more than
a decade or so into the future has not yet been confidently done although
assessments using planetary synodic periods appear to be relevant 7,8.

As displayed in Figure 2, the time-integral of sunspot
number anomalies alone appears to show the estimated true average global temperature
trend (the net average global energy trend) during the planet warm up from the
depths of the Little Ice Age.

The net effect of ocean oscillations is to cause the surface
temperature trend to oscillate above and below the trend calculated using only
the sunspot number anomaly time-integral. Equation (2) accounts for both and also,
because it matches measurements so well, shows that rational change to the level
of atmospheric carbon dioxide can have no significant influence.

Long term prediction of average global temperatures depends
primarily on long term prediction of sunspot numbers.